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4024/11 May/Jun 2020, Question 23: Pattern Sequences and Special Sequences

Cambridge O Level Mathematics 4024 · Paper 11 (Non-calculator) · Non-calculator · 5 marks

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The question, in short

Use the nth term 2n³ to find the 3rd term, then work with the sequence 4/3, 9/5, 16/7, 25/9 to find its next term and an nth term formula.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (a) · 1 mark

Substitute n = 3 into 2n³ and calculate the value of the 3rd term.

  1. 13rd term = 2 × 3³ = 2 × 27 = 54

Answer54

Part (bi) · 1 mark

Identify the pattern in 4/3, 9/5, 16/7, 25/9 and state the fifth term.

  1. 1Numerators 4, 9, 16, 25, 36 (square numbers); denominators 3, 5, 7, 9, 11
  2. 2Next term = 36/11

Answer36/11

Part (bii) · 3 marks

Find an expression in n that generates the terms 4/3, 9/5, 16/7, 25/9.

  1. 1Numerators: 2², 3², 4², 5², … = (n + 1)²
  2. 2Denominators 3, 5, 7, 9 go up by 2: 2n + 1
  3. 3nth term = (n + 1)²/(2n + 1)

Answer((n+1)²)/(2n+1)

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